Sprinkle dry rub generously on all sides of pork roast and place meat into a heavy pan or Dutch oven.
Pour 1/4 teaspoon of liquid smoke flavoring into each of two 6-ounce ramekins; fill ramekins with 1/2 cup water each. Place ramekins into the Dutch oven on either side of the roast. Place lid onto Dutch oven.
Roast pork in the preheated oven until very tender, 12 hours. Remove roast from Dutch oven, place onto a work surface (such as a cutting board), and separate the meat from the bone using your fingers. Discard any large pieces of fat.
Roughly chop pork with a large knife or cleaver; drizzle with 3/4 cup barbeque sauce. Season with salt and black pepper.
Spread about 1 tablespoon barbeque sauce onto each bun and pile pork on buns to serve.